热方程的改进哈密顿矩阵估计值

arXiv - MATH - Differential Geometry Pub Date : 2024-09-16 DOI:arxiv-2409.10379

Lang Qin, Qi S. Zhang

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引用次数: 0

摘要

在本文中，我们取消了汉密尔顿对全闭合流形上热方程的矩阵哈纳克估计中对里奇曲率梯度的假设，回答了一个自 20 世纪 90 年代以来一直存在的问题。新内容包括最近的尖锐李-尤估计、合适向量场的构建以及积分论证、迭代和少量张量代数的各种使用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An improved Hamilton matrix estimates for the heat equation

In this paper, we remove the assumption on the gradient of the Ricci curvature in Hamilton's matrix Harnack estimate for the heat equation on all closed manifolds, answering a question which has been around since the 1990s. New ingredients include a recent sharp Li-Yau estimate, construction of a suitable vector field and various use of integral arguments, iteration and a little tensor algebra.

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arXiv - MATH - Differential Geometry

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